The large-Nc limit of borelized spectral sum rules and the slope of radial Regge trajectories

TL;DR

This paper introduces a new phenomenological method based on large-Nc borelized spectral sum rules to calculate the slope of radial meson trajectories, revealing near-universal values around 1.4 GeV^2.

Contribution

It presents a novel approach extending spectral sum rules to large-Nc, enabling calculation of radial trajectory slopes from ground states and condensates.

Findings

Slopes are approximately universal at 1.4±0.1 GeV^2.

Method predicts the second radial trajectory near 0.6 GeV.

Approach applies to light non-strange mesons.

Abstract

We put forward a new phenomenological method for calculating the slope of radial trajectories from values of ground states and vacuum condensates. The method is based on a large-$N_c$ extension of borelized spectral sum rules. The approach is applied to the light non-strange vector, axial, and scalar mesons. The extracted values of slopes proved to be approximately universal and are in the interval $1.4\pm0.1$ GeV$^2$. As a by-product, the given method leads to prediction of the second radial trajectory with ground state mass lying near 0.6 GeV.